Exponentially Decaying Heat Source on MHD Tangent Hyperbolic Two-Phase Flows over a Flat Surface with Convective Conditions

2018 ◽  
Vol 387 ◽  
pp. 286-295 ◽  
Author(s):  
S.U. Mamatha ◽  
Chakravarthula S.K. Raju ◽  
Putta Durga Prasad ◽  
K.A. Ajmath ◽  
Mahesha ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Weissenberg Number ◽  
Dust Particles ◽  
Convective Conditions ◽  
Two Phase ◽  
Velocity Boundary Layer

The present framework addresses Darcy-Forchheimer steady incompressible magneto hydrodynamic hyperbolic tangent fluid with deferment of dust particles over a stretching surface along with exponentially decaying heat source. To control the thermal boundary layer Convective conditions are considered. Appropriate transformations were utilized to convert partial differential equations (PDEs) into nonlinear ordinary differential equations (NODEs). To present numerical approximations Runge-Kutta Fehlberg integration is implemented. Computational results of the flow and energy transport are interpreted for both fluid and dust phase with the support of graph and table illustrations. It is found that non-uniform inertia coefficient of porous medium decreases velocity boundary layer thickness and enhances thermal boundary layer. Improvement in Weissenberg number improves the velocity boundary layer and declines the thermal boundary layer.

scholarly journals Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 248 ◽  
Author(s):  
Anwar Saeed ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Muhammad Jawad ◽  
Asad Ullah ◽  
...  
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Film Flow ◽  
Three Dimensional ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
The Impact

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

Two-Phase Flow of Dusty Casson Fluid with Cattaneo-Christov Heat Flux and Heat Source Past a Cone, Wedge and Plate

2018 ◽  
Vol 387 ◽  
pp. 625-639 ◽  
Author(s):  
B. Mahanthesh ◽  
Oluwole Daniel Makinde ◽  
Bijjanal Jayanna Gireesha ◽  
Koneri L. Krupalakshmi ◽  
Isaac Lare Animasaun
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Heat Source ◽  
Regression Line ◽  
Casson Fluid ◽  
Temperature Fields ◽  
Dust Particles ◽  
Integration Scheme ◽  
Physical Parameters ◽  
Two Phase

This article addresses the boundary layer flow and heat transfer in Casson fluid submerged with dust particles over three different geometries (vertical cone, wedge and plate). The aspects of Cattaneo-Christov heat flux and exponential space-based heat source (ESHS) are also accounted. At first, the partial differential equations are transformed into a set of ordinary differential equations via appropriate similarity transformations. Resulting equations are solved via shooting method coupled with the Runge-Kutta-Fehlberg-45 integration scheme. The consequences of dimensionless parameters on velocity and temperature fields of both fluid and dust particles phase are analyzed. The rate of increment/decrement in the skin friction as well as the Nusselt number for various values of physical parameters are also estimated via slope of linear regression line using data points.

scholarly journals Hall Effect on Two-Phase Laminar Boundary Layer flow of Dusty Liquid due to Stretching of an Elastic Flat Sheet

2017 ◽  
Vol 16 (3) ◽  
pp. 13-26 ◽  
Author(s):  
B Mahanthesh
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Layer Growth ◽  
Dust Particles ◽  
Two Phase ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
Layer Flow ◽  
Fifth Order ◽  
Boundary Layer Growth

The present investigation is concerned with the effect of Hall current on boundary layer two-phase flow of an electrically conducting dusty fluid over a permeable stretching sheet in the presence of a strong magnetic field. The boundary layer approximation is employed for mathematical modeling. The governing partial differential equations are reduced to a set of ordinary differential equations using suitable similarity transformations. Subsequent equations are solved numerically by using Runge-Kutta-Fehlberg fourth-fifth order method. A comprehensive parametric study is conducted to reveal the tendency of solutions. It is found that the mass concentration of dust particles can be used as a control parameter to control the friction factor at the sheet. The influence of suction and injection are opposite on the momentum boundary layer growth.

scholarly journals Two-Phase Dusty Fluid Flow Along a Rotating Axisymmetric Round-Nosed Body

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Sadia Siddiqa ◽  
Naheed Begum ◽  
M. A. Hossain ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Boundary Layer ◽  
Flow Characteristics ◽  
Leading Edge ◽  
Solid Particles ◽  
Dust Particles ◽  
Computational Domain ◽  
Two Phase ◽  
Carrier Fluid ◽  
Boundary Layer Equations ◽  
Implicit Finite Difference

This article is concerned with the class of solutions of gas boundary layer containing uniform, spherical solid particles over the surface of rotating axisymmetric round-nosed body. By using the method of transformed coordinates, the boundary layer equations for two-phase flow are mapped into a regular and stationary computational domain and then solved numerically by using implicit finite difference method. In this study, a rotating hemisphere is used as a particular example to elucidate the heat transfer mechanism near the surface of round-nosed bodies. We will investigate whether the presence of dust particles in carrier fluid disturbs the flow characteristics associated with rotating hemisphere or not. A comprehensive parametric analysis is presented to show the influence of the particle loading, the buoyancy ratio parameter, and the surface of rotating hemisphere on the numerical findings. In the absence of dust particles, the results are graphically compared with existing data in the open literature, and an excellent agreement has been found. It is noted that the concentration of dust particles’ parameter, Dρ, strongly influences the heat transport rate near the leading edge.

Effects of Viscoelastic Oil-Based Nanofluids on a Porous Nonlinear Stretching Surface with Variable Heat Source/Sink

2018 ◽  
Vol 387 ◽  
pp. 260-272
Author(s):  
Christian John Etwire ◽  
Ibrahim Yakubu Seini ◽  
Rabiu Musah ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Layer Thickness ◽  
Fourth Order ◽  
Boundary Layer Thickness ◽  
Stretching Surface ◽  
Variable Heat ◽  
Nonlinear Stretching

The effect of variable heat source on viscoelastic fluid of CuO-oil based nanofluid over a porous nonlinear stretching surface is analyzed. The problem was modelled in the form of partial differential equations and transformed into a coupled fourth order ordinary differential equations by similarity techniques. It was further reduced to a system of first order ordinary differential equations and solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. The results for various controlling parameters have been tabulated and the flow profiles graphically illustrated. The study revealed that the viscoelastic parameter has a decreasing effect on the magnitude of both the skin friction coefficient and the rate of heat transfer from the surface. It enhanced the momentum boundary layer thickness whilst adversely affecting the thermal boundary layer thickness.

Experimental studies of the viscous boundary layer properties in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 605 ◽  
pp. 79-113 ◽  
Author(s):  
CHAO SUN ◽  
YIN-HAR CHEUNG ◽  
KE-QING XIA
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Rayleigh Number ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Viscous Sublayer ◽  
Viscous Boundary Layer ◽  
Velocity Boundary Layer ◽  
Viscous Boundary

We report high-resolution measurements of the properties of the velocity boundary layer in turbulent thermal convection using the particle image velocimetry (PIV) technique and measurements of the temperature profiles and the thermal boundary layer. Both velocity and temperature measurements were made near the lower conducting plate of a rectangular convection cell using water as the convecting fluid, with the Rayleigh number Ra varying from 109 to 1010 and the Prandtl number Pr fixed at 4.3. From the measured profiles of the horizontal velocity we obtain the viscous boundary layer thickness δυ. It is found that δυ follows the classical Blasius-like laminar boundary layer in the present range of Ra, and it scales with the Reynolds number Re as δυ/H = 0.64Re−0.50±0.03 (where H is the cell height). While the measured viscous shear stress and Reynolds shear stress show that the boundary layer is laminar for Ra < 2.0 × 1010, two independent extrapolations, one based on velocity measurements and the other on velocity and temperature measurements, both indicate that the boundary layer will become turbulent at Ra ~ 1013. Just above the thermal boundary layer but within the mixing zone, the measured temperature r.m.s. profiles σT(z) are found to follow either a power law or a logarithmic behaviour. The power-law fitting may be slightly favoured and its exponent is found to depend on Ra and varies from −0.6 to −0.77, which is much larger than the classical value of −1/3. In the same region, the measured profiles of the r.m.s. vertical velocity σw(z) exhibit a much smaller scaling range and are also consistent with either a power-law or a logarithmic behaviour. The Reynolds number dependence of several wall quantities is also measured directly. These are the wall shear stress τw ~ Re1.55, the viscous sublayer δw ~ Re−0.91, the friction velocity uτ ~ Re0.80, and the skin-friction coefficient cf ~ Re−0.34. All of these scaling properties are very close to those predicted for a classical Blasius-type laminar boundary layer, except that of cf. Similar to classical shear flows, a viscous sublayer is also found to exist in the present system despite the presence of a nested thermal boundary layer. However, velocity profiles normalized by wall units exhibit no obvious logarithmic region, which is likely to be a result of the very limited distance between the edge of the viscous sublayer and the position of the maximum velocity. Compared to traditional shear flows, the peak position of the wall-unit-normalized r.m.s. profiles is found to be closer to the plate (at z+ = z/δw ≃ 5). Our overall conclusion is that a Blasius-type laminar boundary condition is a good approximation for the velocity boundary layer in turbulent thermal convection for the present range of Rayleigh number and Prandtl number.

scholarly journals MHD Laminar Boundary Layer Flow of a Jeffrey Fluid Past a Vertical Plate Influenced by Viscous Dissipation and a Heat Source/Sink

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1896
Author(s):  
Hillary Muzara ◽  
Stanford Shateyi
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Viscous Dissipation ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Vertical Plate ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Layer Flow

This study investigates the effects of viscous dissipation and a heat source or sink on the magneto-hydrodynamic laminar boundary layer flow of a Jeffrey fluid past a vertical plate. The governing boundary layer non-linear partial differential equations are reduced to non-linear ordinary differential equations using suitable similarity transformations. The resulting system of dimensionless differential equations is then solved numerically using the bivariate spectral quasi-linearisation method. The effects of some physical parameters that include the Schmidt number, Eckert number, radiation parameter, magnetic field parameter, heat generation parameter, and the ratio of relaxation to retardation times on the velocity, temperature, and concentration profiles are presented graphically. Additionally, the influence of some physical parameters on the skin friction coefficient, local Nusselt number, and the local Sherwood number are displayed in tabular form.

scholarly journals Effectiveness of Hall current and exponential heat source on unsteady heat transport of dusty TiO2-EO nanoliquid with nonlinear radiative heat

2019 ◽  
Vol 6 (4) ◽  
pp. 551-561 ◽  
Author(s):  
Basavarajappa Mahanthesh ◽  
Nagavangala Shankarappa Shashikumar ◽  
Bijjanal Jayanna Gireesha ◽  
Isac Lare Animasaun
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Heat Source ◽  
Friction Factor ◽  
Skin Friction ◽  
Heat Transport ◽  
Radiative Heat ◽  
Hall Current ◽  
Dust Particles ◽  
Numeric Data

Abstract The problem of exponential heat source across a flowing nanofluid (TiO2-EO; titanium oxide-Engine oil) containing tiny dust particles on a deformable planar plate has been an open question in meteorology. In this paper, the boundary layer transient two-phase flow of dusty nanoliquid on an isothermal plate which is deforming with time-dependent velocity in the presence of exponential heat source is studied. The impacts of Hall current, nonlinear radiative heat and an irregular heat source (temperature based heat source and exponential space-based heat source) are also accounted. Dusty nanofluid is the composition of dust particles and nanoliquid (TiO2-EO). Using relevant transformations, the system of PDEs is rehabilitated to the system of ODEs and then treated numerically. Exploration of the impacts of pertinent parameters on velocity and temperature fields is performed via graphical illustrations. Numeric data for skin friction factor and the Nusselt number is presented and their characteristics are analyzed/quantified through the slope of linear regression via data points. Highlights Boundary layer flow of dusty nanoliquid past a isothermal plate is studied. Impacts of Hall current and irregular heat source are also accounted. Role of physical parameters are focused in momentum and heat transport distributions. Numeric data for skin friction factor and the Nusselt number is presented.

scholarly journals Three-dimensional MHD boundary layer flow due to an axisymmetric shrinking sheet with radiation, viscous dissipation and heat source/sink

2016 ◽  
Vol 21 (2) ◽  
pp. 393-406
Author(s):  
M. Madhu ◽  
B. Balaswamy ◽  
N. Kishan
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Shrinking Sheet ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Source Sink ◽  
Mhd Boundary Layer Flow

AbstractAn analysis is made to study a three dimensional MHD boundary layer flow and heat transfer due to a porous axisymmetric shrinking sheet. The governing partial differential equations of momentum and energy are transformed into self similar non-linear ordinary differential equations by using the suitable similarity transformations. These equations are, then solved by using the variational finite element method. The flow phenomena is characterised by the magnetic parameterM, suction parameterS, porosity parameterKp, heat source/sink parameterQ, Prandtl number Pr, Eckert number Ec and radiation parameterRd. The numerical results of the velocity and temperature profiles are obtained and displayed graphically.

scholarly journals Effects of Mass Suction on MHD Boundary Layer Flow and Heat Transfer over a Porous Shrinking Sheet with Heat Source/Sink

2019 ◽  
Vol 8 (10) ◽  
pp. 263-266 ◽  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Shrinking Sheet ◽  
Dynamic Framework ◽  
Mhd Boundary Layer ◽  
Source Sink

An examination is made to think about the impacts of the mass suction on the steady flow of 2-D magneto-hydrodynamic (MHD) boundary layer flows and heat transfer past on a shrinking sheet with source/sink. In the dynamic framework, an-uniform magnetic field acts perpendicular to the plane of flow. The governing non-dimensional partial differential equations are changed into nonlinear ordinary differential equations (ODE’s) using similarity transformations. The so derived ordinary differential equations are solved numerically by using the MAT LAB solver bvp5c. From the keen examinations it is found that the velocity inside the boundary layer increments with increment of wall mass suction, magnetic field and reportedly the thickness of the momentum layer diminishes. There is a reduction in temperature as increases the Prandtl number. With heat source specifications, Hartmann number, heat sink parameter & the temperature increments are seen. Moreover, for strong heat source heat assimilation at the sheet happens.

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